Least Common Multiple (LCM) of 132 and 97
The least common multiple (LCM) of 132 and 97 is 12804.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 132 and 97?
First, calculate the GCD of 132 and 97 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 132 ÷ 97 = 1 remainder 35 |
| 2 | 97 ÷ 35 = 2 remainder 27 |
| 3 | 35 ÷ 27 = 1 remainder 8 |
| 4 | 27 ÷ 8 = 3 remainder 3 |
| 5 | 8 ÷ 3 = 2 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 159 | 27825 |
| 40 and 67 | 2680 |
| 93 and 44 | 4092 |
| 109 and 30 | 3270 |
| 100 and 156 | 3900 |